We revisit the question whether the running-mass inflation model allows the formation of Primordial Black Holes (PBHs) that are sufficiently long-lived to serve as candidates for Dark Matter. We incorporate recent cosmological data, including the WMAP 7-year results. Moreover, we include "the running of the running" of the spectral index of the power spectrum, as well as the renormalization group "running of the running" of the inflaton mass term. Our analysis indicates that formation of sufficiently heavy, and hence long-lived, PBHs still remains possible in this scenario. As a by-product, we show that the additional term in the inflaton potential still does not allow significant negative running of the spectral index.The Cosmic Microwave Background (CMB) is very smooth. Full-sky observations allow to expand the measured CMB temperature in spherical harmonics Y ℓm . One can then determine the size of the anisotropies as a function of ℓ, with larger ℓ corresponding to smaller angles, and hence smaller length scales. Current CMB observation probe this power spectrum down to (comoving) length scales of about one Mpc. These observations imply very small primordial density perturbations at such large length scales, characterized by the power P Rc ≃ 10 −9 .However, it is possible that the primordial density perturbations become much larger at smaller length scales, beyond the range probed by cosmological observations. Indeed, it is conceivable that these perturbations are so large that overdense regions collapse to form Primordial Black Holes (PBHs) just after the end of inflation [1,2,3]. They are called "primordial" since they do not originate from the gravitational collapse of burnt-out stars; they could thus have any mass, including masses well below or well above stellar masses. Here we assume that the fluctuations which sourced the PBHs are also generated during inflation, specifically towards the end of inflation, well after the length scales probed by conventional cosmological observations exited the horizon.There are various constraints on PBH formation. For example, the density of roughly stellar mass black holes has to satisfy limits from searches for microlensing. Very light black holes could have evaporated (via Hawking radiation) in the epoch of Big Bang nucleosynthesis, altering the predicted isotope abundances. These and other constraints have recently been compiled in [4]. They can be translated into upper limits on the amplitude of the power spectrum at the length scales relevant for PBH formation, typically P Rc < 10 −2 − 10 −1 with some scale dependence.Clearly the power spectrum has to change dramatically towards the end of inflation for PBH formation to occur. In the framework of standard slow-roll inflation, this implies that the slowroll parameters, and hence the inflaton potential, also should show large variations. One simple, and yet well motivated, model that can feature large variations of the slow-roll parameters is the running-mass model [5,6], a type of inflationary model which emerges ...
A broad range of single field models of inflation are analyzed in light of all relevant recent cosmological data, checking whether they can lead to the formation of long-lived Primordial Black Holes (PBHs). To that end we calculate the spectral index of the power spectrum of primordial perturbations as well as its first and second derivatives. PBH formation is possible only if the spectral index increases significantly at small scales, i.e. large wave number k. Since current data indicate that the first derivative α S of the spectral index n S (k 0 ) is negative at the pivot scale k 0 , PBH formation is only possible in the presence of a sizable and positive second derivative ("running of the running") β S . Among the three small-field and five large-field models we analyze, only one smallfield model, the "running mass" model, allows PBH formation, for a narrow range of parameters. We also note that none of the models we analyze can accord for a large and negative value of α S , which is weakly preferred by current data.
In this work we study the chromo-natural inflation model in the anisotropic setup. Initiating inflation from Bianchi type-I cosmology, we analyze the system thoroughly during the slow-roll inflation, from both analytical and numerical points of view. We show that the isotropic FRW inflation is an attractor of the system. In other words, anisotropies are damped within few efolds and the chromo-natural model respects the cosmic no-hair conjecture. Furthermore, we demonstrate that in the slow-roll limit, the anisotropies in both chromo-natural and gauge-flation models share the same dynamics.PACS numbers: 98.80.Cq
The study started in Ref. [16] about the Dilaton mean field stabilization thanks to the effective potential generated by the existence of massive fermions, is here extended. Three loop corrections are evaluated in addition to the previously calculated two loop terms. The results indicate that the Dilaton vacuum field tend to be fixed at a high value close to the Planck scale, in accordance with the need for predicting Einstein gravity from string theory. The mass of the Dilaton is evaluated to be also a high value close to the Planck mass, which implies the absence of Dilaton scalar signals in modern cosmological observations. These properties arise when the fermion mass is chosen to be either at a lower bound corresponding to the top quark mass, or alternatively, at a very much higher value assumed to be in the grand unification energy range. One of the three 3-loop terms is exactly evaluated in terms of Master integrals. The other two graphs are however evaluated in their leading logarithm correction in the perturbative expansion. The calculation of the non leading logarithmic contribution and the inclusion of higher loops terms could made more precise the numerical estimates of the vacuum field value and masses, but seemingly are expected not to change the qualitative behavior obtained. The validity of the here employed Yukawa model approximation is argued for small value of the fermion masses with respect to the Planck one. A correction to the two loop calculation done in the previous work is here underlined.
We study the possibility that particle production during inflation can source the required power spectrum for dark matter (DM) primordial black holes (PBH) formation. We consider the scalar and the gauge quanta production in inflation models, where in the latter case, we focus in two sectors: inflaton coupled i) directly and ii) gravitationally to a U (1) gauge field. We do not assume any specific potential for the inflaton field. Hence, in the gauge production case, in a model independent way we show that the non-production of DM PBHs puts stronger upper bound on the particle production parameter. Our analysis show that this bound is more stringent than the bounds from the bispectrum and the tensor-to-scalar ratio derived by gauge production in these models. In the scenario where the inflaton field coupled to a scalar field, we put an upper bound on the amplitude of the generated scalar power spectrum by non-production of PBHs. As a by-product we also show that the required scalar power spectrum for PBHs formation is lower when the density perturbations are non-Gaussian in comparison to the Gaussian density perturbations. * erfani@iasbs.ac.ir 1 arXiv:1511.08470v2 [astro-ph.CO] 17 Apr 2016Inflation is currently the standard paradigm for solving the cosmological puzzles of the standard big bang cosmology, such as homogeneity, isotropy and flatness of the universe. In addition, the quantum fluctuation of the inflaton field explain the generation of all (classical) inhomogeneities that can be seen in our universe, from the Cosmic Microwave Background (CMB) anisotropies to the Large Scale Structure (LSS) [1]. In the simplest models, inflaton field slowly rolls down its potential, however, generically the inflaton should be expected to couple to some additional degrees of freedom and a variety of different models have been proposed. 1 Recently, inflation models where production of some non-inflaton particles happens during inflation via parametric resonance has received a lot of attention 2 [3,4,5,6,8,9,10]. In this class of models, the inflaton field couples to another field directly or gravitationally and the coupled field can be massless or massive fermion [3], scalar [4,5,7] or gauge field [11,12,13]. The production of light species occurs during inflation at the expenses of the kinetic energy of the inflaton and slows down its motion; i.e. resonant extraction of inflaton field energy decreasesφ, leading to an increase in the scalar power spectrum, P ζ ∝ H 4 /φ 2 . It was shown that the production of particles during inflation provides a qualitatively new mechanism for generating cosmological perturbations [3,6,8]. The nature of these fluctuations is usually non-scale-invariant and non-Gaussian (NG) [12,13,14,15].A particular feature is that the power spectrum of these fluctuations can be very blue; this means that the amplitude of density fluctuations can be much higher at the small length scales relevant for Primordial Black Holes (PBHs) formation [16,17]. To be consistent with cosmological observations such as ...
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